Analyzing the second derivative to find inflection points

Find inflection points by analyzing the second derivative (article) | Khan Academy. Math · AP®︎/College Calculus AB · Applying derivatives to analyze functions · Determining concavity
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Inflection points introduction (video)

An inflection point exists at a given x -value only if there is a tangent line to the function at that number. This is the case wherever the first derivative exists or where there’s a

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Inflection Point Definition

The derivative is y' = 15x2 + 4x − 3. The second derivative is y'' = 30x + 4. And 30x + 4 is negative up to x = −4/30 = −2/15, positive from there onwards. So: f (x) is concave downward up to x =

4.2.2 How to find inflection points when given a formula

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Inflection Points

Math · AP®︎/College Calculus AB · Applying derivatives to analyze functions · Determining concavity of intervals and finding points of inflection: algebraic Inflection points review

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